scholarly journals The Godunov-inverse iteration: A fast and accurate solution to the symmetric tridiagonal eigenvalue problem

2005 ◽  
Vol 54 (2) ◽  
pp. 208-221 ◽  
Author(s):  
Anna M. Matsekh
Keyword(s):  
Eigenvalue Problem ◽  
Accurate Solution ◽  
Inverse Iteration

scholarly journals A Multilevel Correction Scheme for the Steklov Eigenvalue Problem

2015 ◽  
Vol 2015 ◽  
pp. 1-11
Author(s):  
Qichao Zhao ◽  
Yidu Yang ◽  
Hai Bi
Keyword(s):  
Theoretical Analysis ◽  
Eigenvalue Problem ◽  
Numerical Experiments ◽  
Inverse Iteration ◽  
Correction Technique ◽  
Correction Scheme ◽  
Multiple Eigenvalues ◽  
Steklov Eigenvalue ◽  
Steklov Eigenvalue Problem

Combining the correction technique proposed by Lin and Xie and the shifted inverse iteration, a multilevel correction scheme for the Steklov eigenvalue problem is proposed in this paper. The theoretical analysis and numerical experiments indicate that the scheme proposed in this paper is efficient for both simple and multiple eigenvalues of the Steklov eigenvalue problem.

scholarly journals Towards a Method for the Accurate Solution of the Schrödinger Wave Equation in Many Variables. I. Formulation of the Method for an Eigenvalue Problem without Symmetry Conditions

1959 ◽  
Vol 12 (4) ◽  
pp. 430
Author(s):  
IM Bassett
Keyword(s):  
Wave Equation ◽  
Eigenvalue Problem ◽  
Digital Computer ◽  
Accurate Solution ◽  
New Method ◽  
Electronic Digital Computer

The aim of this paper and those following is to formulate and explore a new method, suitable for use with an electronic digital computer, for the solution of eigenvalue. eigenfunction problems in many variables, with the aim of applying the method to the Schrodinger wave equation.

scholarly journals Towards a Method for the Accurate Solution of the Schrödinger Wave Equation in Many Variables. II. A Simple Numerical Illustration

1959 ◽  
Vol 12 (4) ◽  
pp. 441 ◽  
Author(s):  
IM Bassett
Keyword(s):  
Wave Equation ◽  
Eigenvalue Problem ◽  
Accurate Solution ◽  
Numerical Illustration

The method described in Part I is here applied to an eigenvalue problem in two Variables

scholarly journals Решение обратной задачи для сложного вибронного аналога резонанса Ферми на основе плоских вращений Якоби

2020 ◽  
Vol 128 (11) ◽  
pp. 1614
Author(s):  
В.А. Кузьмицкий
Keyword(s):  
Eigenvalue Problem ◽  
Spectral Data ◽  
Similarity Transformation ◽  
Accurate Solution ◽  
Fermi Resonance ◽  
Matrix Elements ◽  
Second Stage ◽  
The Matrix ◽  
Two Stages ◽  
Orthogonal Similarity Transformation

Based on algebraic methods, we have found an accurate solution for the inverse task for the vibronic analogue of the complex Fermi resonance, i.e. the determination from the spectral data (energies Ek and transition intensities Ik of the observed conglomerate of lines, k = 1, 2, ..., n; n > 2) energies of the «dark» states Am and the matrix elements of their coupling Bm with the «bright» state. The algorithm consists of two stages. At the first stage, the Jacobi plane rotations are used to construct an orthogonal similarity transformation matrix X, for which the elements of the first row obey the requirement (X1k)^2 = Ik, which corresponds to that fact that there is only one non-perturbed «bright» state. At the second stage, the quantities Am and Bm are obtained after solving the eigenvalue problem for block of «dark» states of the matrix Xdiag({Ek})X-1.

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